As a large manager of currency overlays, SSgA is often asked by clients to suggest an appropriate hedge ratio for international equity portfolios. Setting an optimal, forward-looking hedge ratio is difficult; it is always so much easier to do with hindsight. However, in seeking to answer this question, we are often faced with the assumption that hedging removes currency risk. This assumption is further supported by a number of industry standard equity risk models that suggest most currency hedged equity portfolios have a lower overall level of currency risk than unhedged portfolios.

In this essay we perform rudimentary tests on actual historic outcomes from hedging to see if experience has matched the theory. Conveniently, the MSCI World Hedged Index^SM series had its 20th birthday in December 2007, providing our dataset. While the analysis extends the full 20 years, we also show results over 5 year periods to reflect the time horizons over which many institutional investors appear to operate.

One Man's Meat is Another Man's Poison
An investor who purchases shares in a country other than his own is normally exposed to both positive and negative returns associated with that country's equity market, as well as positive and negative returns associated with that country's currency. In a fully hedged international equity portfolio, the returns associated with currency movements are largely removed.

At this point it is worth reflecting briefly on the mechanics of hedging. A European investor who hedges the currency exposure of a US equity portfolio usually does so by executing the following forward foreign exchange contract:

On the other hand, a US investor who hedges the currency exposure of a European equity portfolio does the opposite:

Both investors are executing a currency hedge, and yet the trades are diametrically opposed. Herein lies one of the complexities of analyzing currency hedges; an optimal hedge ratio (however that is defined) for one currency is unlikely to be optimal for another. Analysis of currency hedging is often prepared with one particular base currency either implicitly or explicitly in mind, and it is dangerous to translate the results to another base currency.

In the remainder of this essay, we have largely ignored hedging returns. This is partly because returns are so difficult to forecast, and partly because by definition one base currency's positive hedge return means a negative in another currency. Rather we have focused on risk and, more specifically, volatility. Has currency hedging historically reduced portfolio volatility, and have the results been influenced by base currency?

Of course, volatility is only one of the many possible definitions of risk. At the end of this essay, we comment on other measures of risk, but the bulk of this essay focuses on realized volatility.

Defining International Portfolios
The risk results that follow have been adjusted to reflect typical currency exposures for an international portfolio. For example, currently an international equity portfolio for an Australian investor that is benchmarked against a developed markets capitalization weighted index will have a basket currency exposure of roughly 50% to the USD, 18% to EUR, 11% to GBP, 10% to JPY and so on. An international equities portfolio for a US investor however will have nil to USD and roughly 33% to EUR, 21% to GBP, 20% to JPY and so on.

Currency Only Risk
Figure 1 shows the rolling 5 year currency volatility of an international equity portfolio for a range of base currency investors. The volatility of global equities, as measured by local market returns, has also been shown for reference.

From Figure 1 it is evident that;

• Currency volatility has been lower than equity market volatility, and has converged and trended down over recent years.
• The spike in rolling 5 year volatility for JPY base investors reflects the sudden appreciation of the JPY in September and October 1998 where the JPY strengthened 21% against the USD in two months.
• An upwards spike in recent volatility is evident for the AUD in particular.
• There are appreciable differences in currency volatility for different base currency investors.

Correlation with Equity Markets
In determining whether currency adds to overall portfolio risk, it is necessary to consider not only the absolute level of currency risk, but also whether, for each base currency, movements in the relevant basket of overseas currencies are correlated with overseas equity market movements. Figure 2 explores this by examining the correlation between international equity market returns and currency basket returns.

Given one man's meat is another man's poison, it is not surprising that in some circumstances currency movements are negatively correlated with equity market movements and in others they are positively correlated.

At +/-20%, most of the correlation results in Figure 2 are not particularly significant. The strong negative correlation of currency and equity market movements for AUD base investors is, however, of particular interest. Anecdotally, the linkage may be associated with the market's view on global growth. Given the sizeable contribution commodities make to Australia's economy, a bullish view on growth that is reflected in equity market appreciation is also reflected in an appreciating AUD. However, for an AUD base investor, the appreciating AUD is bad news for international holdings with non-AUD currency exposures. Hence the negative correlation between equity and currency market movements.

Incremental Volatility from Hedging
Having viewed currency volatility in isolation and the correlation between monthly currency movements and equity market movements, the final step is to bring these two elements together to assess the overall impact of currency hedging on equity portfolio volatility. Figure 3 shows the increase or decrease in rolling 5 year volatility brought about by hedging an "international" equity portfolio. Each data point is calculated as

From Figure 3:

• As a broad rule, it does appear reasonable to assume that currency hedging will, more often than not, reduce the volatility of an international equities portfolio for most base currencies.
• Given equity market volatility of 10% to 20% per annum, reductions of 1% to 2% per annum for USD and GBP base investors are noticeable, but hardly dramatic.
• There have been extended periods for AUD base currency investors where currency hedging has actually increased volatility. This is primarily due to the negative correlation between equity market movements and currency movements for AUD investors.

Other Considerations
Incremental Returns
Figure 4 shows the incremental returns from currency hedging, as opposed to the incremental risk shown in the previous section.

Again, given one man's meat is another's poison, one would expect the results to be distributed evenly around the horizontal axis, and that is in fact the case. What is interesting is the magnitude of the results. While risk reductions seem to range from 0% pa to 5% per annum, return impacts of 5% per annum to 15% per annum over 5 year periods are observed. To express this differently, the impact on total portfolio value of hedging for AUD investors over the 5 years to 31 December 2007 was +57%, while the impact for JPY investors over the 5 years to 31 July 1998 was -35%. For those with views on future currency directions, return outcomes will often swamp volatility when setting hedge ratios.

Many long-term investors would argue, and not without reason, that risk of unrecoverable capital loss is of more concern than volatility in month-to-month results. Analysis of tail risk events, or identification of valuation extremes, may lead to different conclusions on the role of currency hedging in a portfolio.

Carry
Given the significance of hedge returns, we provide in Figure 5 one of the components of return in hedge programs. Forward foreign exchange contracts are priced to reflect the difference in short term interest rates. Hence, a US investor hedging exposure to European equities would receive the short-term USD interest rate and pay the short-term EUR interest rate. For currencies with high short-term interest rates, there is a positive "carry" associated with hedging, while for currencies with low short-term interest rates, the "carry" is negative. The chart below shows the rolling 5 year average "carry" for a range of base currencies. Note that the incremental returns in the previous chart were inclusive of interest rate spreads.

Other Portfolio Assets
International equity assets often form part of a more broadly diversified portfolio including domestic equities, fixed income, cash, REITs and so on. A deeper assessment of the role of currency hedging would include interaction with other asset classes; in other words, are there further diversification benefits associated with foreign currency exposures? Currency hedging may only have a marginal impact on volatility for an international portfolio, but may result in lower of negative correlations with domestic assets, leading to lower overall portfolio volatility. The significant variations in what constitutes a typical balanced portfolio for a JPY versus EUR versus USD base currency investor mean that this question needs to be tackled one market at a time, preferably with an eye to tail risks as well as normal month-to-month volatility.

20 Year Results
Figure 6 summarises the returns and risks associated with hedging over the 20 years to 31 December 2007 for a range of base currencies. These results are based on MSCI World indices and are therefore representative of global portfolios (inclusive of the local market) rather than international portfolios.

Equity Risk Models
By way of comparison, Figure 7 shows the impact of currency for different base investors in the MSCI World Index using the BARRA Global Equity Markets model as at 31 March 2008.

The orders of magnitude are similar to the long-term results above, with the notable exception of Japan.

Conclusions
Following are some conclusions that can be drawn in relation to realized volatility;

• For most base currencies, over most periods, hedging seems to have reduced the volatility of international equity portfolios.
• The reductions in volatility are modest at 2%-3% per annum or less, particularly compared to the impact on longer term returns.
• Currency hedging doesn't always reduce realized volatility; for example hedging has actually increased volatility for AUD base currency investors for much of the last 10 years.
• The characteristics of the base currency are likely to play a key role in setting an optimal ratio; Australia's exposure to the commodity cycle and very low interest rates in Japan are two examples.
• To the extent that clients refer to standard mean-variance frameworks for setting hedge ratios, volatilities and correlations can change significantly over 5 year periods.

Posted On: June 24, 2008